Domain: Operations and Algebraic Thinking Standard Code: 2.01.A Teacher Name: Adapted from: Smith, Margaret Schwan, Victoria Bill, and Elizabeth K. Hughes. “Thinking Through a Lesson Protocol: Successfully Implementing High-­‐Level Tasks.” Mathematics Teaching in the Middle School 14 (October 2008): 132-­‐138. CYCLE 1 (This lesson has 2 cycles to be done the same day.) PART 1: SELECTING AND SETTING UP A MATHEMATICAL TASK
What are your mathematical goals for Students will be able to write an equation and subtract a subtraction problem with an unknown change
using multiple strategies.
the lesson? (i.e., what do you want students to know and understand about mathematics as a result of this lesson?)
What are your expectations for students as they work on and complete this task? • What resources or tools will students have to use in their work that will give them entry into, and help them reason through, the task? • How will the students work— independently, in small groups, or in pairs—to explore this task? • How will students record and report their work? How w ill you introduce students to the activity so as to provide access to all students while maintaining the cognitive demands of the task? •
•
•
•
•
Students will recognize that the missing number is the subtrahend and be able to use a symbol
(square, x, question mark, etc.) to represent the missing number in the equation. They will use at
least two strategies to find their answer.
Students will need connecting cubes or counters, paper, and pencil.
Students will work independently or in pairs.
Students will record their work on their paper and report to the class using the document
camera.
Begin lesson by chanting the class “Story Problem Rap” to get students ready to start.
“Understand the problem. Make a plan to solve it. Do it. Go back and check.”
Students will be gathered together and presented verbally and visually (on chart paper) with the
following story:
Jill was at the carnival. She won a bunch of balloons. There were 24 balloons in the bunch. She
accidentally let go and some flew away. When she counted the balloons again, she had 13 left. How
many balloons flew away?
Ask students to think in their minds about what is happening. Do not have them solve it, just think
about it. Have a student restate the problem in his/her own words.
Remind students the 3 things that are expected (write an equation, show 2 strategies, clear answer).
Also remind students you will be looking for efficient strategies to be shared.
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
As students work independently or in • What do you know? What are you trying to find out?
small groups, what questions will you • What action is happening? What equation could you write to represent the story?
ask to— • Is your equation clear? How did you represent the missing balloons?
• help a group get started or make • Is there another way to solve it? Is that the most efficient way to solve this problem?
progress on the task? • focus students’ thinking on the key mathematical ideas in the task? • assess students’ understanding of key mathematical ideas, problem-­‐ solving strategies, or the representations? • advance students’ understanding of the mathematical ideas? All students are required to write an equation that represents the missing subtrahend with a symbol,
How will you ensure that students show 2 strategies, and find the answer on their paper.
remain engaged in the task? • What assistance will you give or • Use the cubes or counters to show what is happening in the problem. Ask again, “What do
what questions will you ask a you know? What are you trying to find out?”
student (or group) who becomes •
Students will be encouraged to use a different strategy to solve the problem. We will also
quickly frustrated and requests have challenge problem on the board that is the same problem with larger numbers.
more direction and guidance is solving the task? • What will you do if a student (or group) finishes the task almost immediately? How will you extend the task so as to provide additional challenge? PART 3: SHARING AND DISCUSSING THE TASK
Partners or individuals will put their paper on the document camera for the whole class to see.
How will you orchestrate the class discussion so that you accomplish your • First, we will have one group who drew a picture share their work.*
mathematical goals? • Next, we will have one group who used a number line to share their work. Process
• Which solution paths do you want above repeated.*
to have shared during the •
Then, we will have a group who used addition to write their equation to share their
class discussion? In what order will work. Make the connection between addition and subtraction.*
the solutions be presented? Why? •
If there are any other strategies the teacher thinks is important to share, have them
• What specific questions will you ask share at this point.*
so that students will— 1. make sense of the *As students are sharing their work, listening students are expected to listen, ask questions,
mathematical ideas that you and make connections. After each presentation, the presenting students will call on a listening
want them to learn? 2. expand on, debate, and question student to repeat their strategy. Teacher will clarify and guide the discussion to bring out the
objective. The questions students/teacher might ask include “Why did you choose that
the solutions being shared? strategy? How did you show the missing balloons in your equation?”
3. make connections among the different strategies that are presented? 4. look for patterns? 5. begin to form generalizations? What will you see or hear that lets you know that all students in the class understand the mathematical ideas that you intended for them to learn?
CYCLE 2 PART 1: SELECTING AND SETTING UP A MATHEMATICAL TASK
What are your mathematical goals for Students will be able to write an equation and subtract a subtraction problem with an unknown change
using multiple strategies.
the lesson? (i.e., what do you want students to know and understand about mathematics as a result of this lesson?)
What are your expectations for students as they work on and complete this task? • What resources or tools will students have to use in their work that will give them entry into, and help them reason through, the task? • How will the students work— independently, in small groups, or in pairs—to explore this task? • How will students record and report their work? How will you introduce students to the activity so as to provide access to all students while maintaining the cognitive demands of the task? •
•
•
•
•
Students will recognize that the missing number is the subtrahend and be able to use a symbol
(square, x, question mark, etc.) to represent the missing number in the equation. They will use at
least two strategies to find their answer.
Students will need connecting cubes or counters, paper, and pencil.
Students will work independently or in pairs.
Students will record their work on their paper and report to the class using the document
camera.
Students will be gathered together and presented verbally and visually (on chart paper) with the
following story:
Jack had 35 marbles. He gave some to his brother. Now he only has 18. How many marbles did he
give to his brother?
Ask students to think in their minds about what is happening. Do not have them solve it, just think
about it. Have a student restate the problem in his/her own words.
Remind students the 3 things that are expected (write an equation, show 2 strategies, clear answer).
Also remind students you will be looking for efficient strategies to be shared. Encourage them to try
strategies that were just presented.
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
As students work independently or in • What do you know? What are you trying to find out? What strategies do you want to try this
small groups, what questions will you time?
ask to— • What action is happening? What equation could you write to represent the story?
• help a group get started or make • Is your equation clear? How did you represent the missing balloons?
progress on the task? • Is there another way to solve it? Is that the most efficient way to solve this problem?
• focus students’ thinking on the key mathematical ideas in the task? • assess students’ understanding of key mathematical ideas, problem-­‐ solving strategies, or the representations? • advance students’ understanding of the mathematical ideas? All students are required to write an equation that represents the missing subtrahend with a symbol,
How will you ensure that students show 2 strategies, and find the answer on their paper.
remain engaged in the task? • What assistance will you give or • Use the cubes or counters to show what is happening in the problem. Ask again, “What do
what questions will you ask a you know? What are you trying to find out?”
student (or group) who becomes •
Students will be encouraged to use a different strategy to solve the problem. We will also
quickly frustrated and requests have challenge problem on the board that is the same problem with larger numbers.
more direction and guidance is solving the task? • What will you do if a student (or group) finishes the task almost immediately? How will you extend the task so as to provide additional challenge? PART 3: SHARING AND DISCUSSING THE TASK
Partners or individuals will put their paper on the document camera for the whole class to see.
How will you orchestrate the class discussion so that you accomplish your • First, we will have one group who drew a picture share their work.*
mathematical goals? • Next, we will have one group who used a number line to share their work. Process
• Which solution paths do you want above repeated.*
to have shared during the •
Then, we will have a group who used addition to write their equation to share their
class discussion? In what order will work. Make the connection between addition and subtraction.*
the solutions be presented? Why? •
If there are any other strategies the teacher thinks is important to share, have them
• What specific questions will you ask share at this point.*
so that students will— 1. make sense of the *As students are sharing their work, listening students are expected to listen, ask questions,
mathematical ideas that you and make connections. After each presentation, the presenting students will call on a listening
want them to learn? 2. expand on, debate, and question student to repeat their strategy. Teacher will clarify and guide the discussion to bring out the
objective. The questions students/teacher might ask include “Why did you choose that
the solutions being shared? strategy? How did you show the missing balloons in your equation?”
3. make connections among the different strategies that are presented? 4. look for patterns? 5. begin to form generalizations? What will you see or hear that lets you know that all students in the class understand the mathematical ideas that you intended for them to learn?